Let me just note here that our most commonly-used conventional
transliteration scheme uses H for Eta rather than A (which we generally use
to represent Alpha); I gather that you're using A because of the English
long-A pronunciation.

>The contextual (introductory formula) perfective present seems to best
>describe LEGEI this way. That is, the statement was spoken in the past, it
>still speaks today and is binding on the hearers. Is LEGEI a Perfective
>Present in Gal 4:30?

I don't see any particular value in terming this a "perfective present";
that makes more sense either with such verbs as hHKW or PAREIMI that have a
semantic force of completed action (or classical Greek ERRW), or the
particular usage of EIMI in a context implying that it must be perfective
(such as TOSOUTWi CRONWi with EIMI in John 14:9). But in Gal 4:30 I see
nothing implicit in the phrasing to underscore the perfective aspect. The
use of the present LEGEI with hH GRAFH is by no means uncommon.

>Secondly, the two genitive phrases (h hUIOS TAS
>PAIDISKAS and TOU hUIOU TAS ELEUTHERAS seem to be genitives of
>relationship. I am not sure because genitives of relationship are so rare
>and I don't know if it meets the level of acceptance of this type here. Is
>it a genitive of relationship or a simple genitive of possession?

Here too I have to say I see no point in seeking a category in which to
pigeonhole what I take to be a simple instance of the standard adnominal
genitive where the meaning of the phrase created by the genitive dependent
on a noun is perfectly clear. Call it "pertinentive" or "possessive" and
have done with it.

>Thirdly,
>I am interested in the presence of OU MA before KLARONOMASEI, what is the
>reason of both, does it have anything to do with seeing KLARONOMASEI as a
>future active indicative or an aorist active imperative? Fourthly, EKBALE
>position in the sentence and in the argument is exceptional, I am thinking
>that it is a permissive imperative or a conditional imperative instead of a
>simple command, any thoughts?

I believe this is a Semitism with imperatival force; one does not
ordinarily find OU MH with the future in classical Attic but it is common
in the LXX, from which this text is being cited--my recollection is that
this is the way the LXX translators conveyed an infinitive absolute
construction (is that the right term? I know very little Hebrew grammar).